Sliding modes in Banach spaces. (English) Zbl 1031.93050

Levaggi, Laura

Differ. Integral Equ. 15, No. 2, 167-189 (2002).

A concept of a generalized solution for autonomous semilinear differential equations (with state-discontinuous right-hand side) in a reflexive Banach space is defined. This definition makes sense for a control system with discontinuous feedback control law and describes its motion on a sliding surface. Under suitable assumptions, it is shown that there exists only one generalized solution which is viable on the sliding surface and coincides with the one arising from the application of the equivalent control method [Yu. V. Orlov and V. I. Utkin, Automatica 23, 753-757 (1987; Zbl 0661.93036)]. The results obtained are applied to an exponential stabilization problem.

Reviewer: Michael I.Krastanov (Sofia)

MSC:

93B12	Variable structure systems
93C25	Control/observation systems in abstract spaces
34A60	Ordinary differential inclusions
34G25	Evolution inclusions
93D15	Stabilization of systems by feedback

Keywords:

sliding mode control; semilinear differential equations; systems in Banach spaces; generalized solution; discontinuous feedback; exponential stabilization

Citations:

Zbl 0661.93036